{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Lab 9b - 2-fold cross validation\n",
    "\n",
    "We will finish Lab 9 in this notebook."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import statsmodels.formula.api as smf\n",
    "import seaborn as sns\n",
    "import numpy as np\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn import datasets, linear_model\n",
    "from sklearn.model_selection import KFold\n",
    "\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>dataset</th>\n",
       "      <th>x</th>\n",
       "      <th>y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>I</td>\n",
       "      <td>10.0</td>\n",
       "      <td>8.04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>I</td>\n",
       "      <td>8.0</td>\n",
       "      <td>6.95</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>I</td>\n",
       "      <td>13.0</td>\n",
       "      <td>7.58</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>I</td>\n",
       "      <td>9.0</td>\n",
       "      <td>8.81</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>I</td>\n",
       "      <td>11.0</td>\n",
       "      <td>8.33</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  dataset     x     y\n",
       "0       I  10.0  8.04\n",
       "1       I   8.0  6.95\n",
       "2       I  13.0  7.58\n",
       "3       I   9.0  8.81\n",
       "4       I  11.0  8.33"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Load the Anscombe quartet data\n",
    "anscombe = sns.load_dataset(\"anscombe\")\n",
    "anscombe.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x</th>\n",
       "      <th>y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>10.0</td>\n",
       "      <td>7.46</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>8.0</td>\n",
       "      <td>6.77</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>13.0</td>\n",
       "      <td>12.74</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>9.0</td>\n",
       "      <td>7.11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>11.0</td>\n",
       "      <td>7.81</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>14.0</td>\n",
       "      <td>8.84</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>6.0</td>\n",
       "      <td>6.08</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>4.0</td>\n",
       "      <td>5.39</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>12.0</td>\n",
       "      <td>8.15</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>7.0</td>\n",
       "      <td>6.42</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>5.0</td>\n",
       "      <td>5.73</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       x      y\n",
       "22  10.0   7.46\n",
       "23   8.0   6.77\n",
       "24  13.0  12.74\n",
       "25   9.0   7.11\n",
       "26  11.0   7.81\n",
       "27  14.0   8.84\n",
       "28   6.0   6.08\n",
       "29   4.0   5.39\n",
       "30  12.0   8.15\n",
       "31   7.0   6.42\n",
       "32   5.0   5.73"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Separate out the Anscombe 3 data\n",
    "anscombe_3 = anscombe[anscombe[\"dataset\"] == \"III\"]\n",
    "anscombe_3 = anscombe_3[[\"x\",\"y\"]]\n",
    "anscombe_3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x11235ab00>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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8HMA3VHW+za/bIyImgBSAN9v4vYk2xQ/bQtYrd7t9n9Ps6adyt7WK2XZvqzZxRi4dqtxu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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11235a828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot Anscombe 3\n",
    "sns.regplot(x = \"x\", y = \"y\", data = anscombe_3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Split the data in half into fold 1 and fold 2\n",
    "X_fold1, X_fold2, y_fold1, y_fold2 = train_test_split(anscombe_3[[\"x\"]], anscombe_3[\"y\"], test_size=0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>9.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>7.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>6.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>4.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>10.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       x\n",
       "25   9.0\n",
       "31   7.0\n",
       "28   6.0\n",
       "29   4.0\n",
       "22  10.0"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_fold1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Use the training data to fit the linear model using the sci-kit learn version:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Use this linear model to make predictions for the fold 2 data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compute the mean squared error for the fold 2 predictions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's do the reverse.  Use the fold2 data to create the linear model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Use this linear model to make predictions for the fold 1 data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compute the mean squared error for the fold 1 predictions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How do the two mean squared errors compare?  What might be happening here?\n",
    "\n",
    "To better understand whaat's happening, let's plot the two training data sets using `regplot()` in Seaborn.  \n",
    "\n",
    "First plot the fold 1 data, where x is `X_fold1[\"x\"]` and y is `y_fold1`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1a1c2255f8>"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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W+ZOZM2WEppFFxBMqBQ+U7jhAUUkpb27eB0B8TBTf/OQEFn1yAolxuuGNiHhH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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112866780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next plot the fold 2 data, where x is `X_fold2[\"x\"]` and y is `y_fold2`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1a1c345400>"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a1c078438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}